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Rollout:

Posted By: Daniel Murphy
Date: Thursday, 21 June 2007, at 8:05 p.m.

In Response To: Rollout: (DC-Ohio)

If white takes the cube, does he reship on any blotting roll by blue?

Yes. White risks very little (the difference between 9-away Crawford and losing) to gain a lot (the difference between an even match at 4-away all and leading 5-away Crawford).

Suppose White estimates 11/36 hits, winning only 80% of the time thereafter, and ignores his chances of getting a second shot. Then White would win ~25% of the time. White's doubling window opens at about 13.5%, and he's well above that.

No Redouble to 8, Lose -> -9,-1 Crawford, ME = 5.4%

Redouble to 8, Lose -> -9, -0, ME = 0%

No Redouble to 8 , Win -> -5,-5, ME = 50%

Redouble to 8, Win -> -1,-5 Crawford, ME = 84.4%

Risk = 5.4%, Gain = 34.4%, R/(R+G) = 5.4/39.9 = 13.5%

Even if Blue rolls 6-6, after which White, if he hits, only wins about 72% of the time (rollout not shown), White should redouble:

The score (after 0 games) is: White 0, Blue 4 (match to 9 points)

Move number 7: White on roll, cube decision?

White85


2X '2X4X2X2X2X ' ' ' ' '

3O4O4O1O ' ' ' ' ' ' ' '

Blue27

Position ID: 914AAGD2tgEACA Match ID: AgEgAQAAIAAA

• White doubles

Cube decision
Rollout cubeless equity -0.5702(Money: -0.6019)
Cubeful equities:
1.Double, take -0.3820
2.Double, pass +1.0000 +1.3820
3.No double -0.4005 -0.0185
Proper cube action:Redouble, take
Rollout details
WinW gW bg LoseL gL bgCubelessCubeful
Player White owns 4-cube0.21990.00000.0000-0.78010.04120.0006 -0.5702 -0.4005
Standard error0.00050.00000.0000-0.00050.00150.0003 0.0010 0.0014
Player Blue owns 8-cube0.22720.00000.0000-0.77280.23710.0002 -0.3820 -0.3820
Standard error0.00120.00000.0000-0.00120.02190.0001 0.0044 0.0044
Full cubeful rollout with var.redn.
216 games, Mersenne Twister dice gen. with seed 1062244923 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Another rollout; Blue has played 6-2:

The score (after 0 games) is: White 0, Blue 4 (match to 9 points)

Move number 7: White on roll, cube decision?

White85


2X '2X4X2X2X2X ' ' ' ' '

3O4O5O1O '2O ' ' ' ' ' '

Blue42

Position ID: 974MAACztw0AQA Match ID: AgEgAQAAIAAA

• White doubles

Cube decision
Rollout cubeless equity -0.3281(Money: -0.3483)
Cubeful equities:
1.Double, take +0.0054
2.Double, pass +1.0000 +0.9946
3.No double -0.2015 -0.2068
Proper cube action:Redouble, take
Rollout details
WinW gW bg LoseL gL bgCubelessCubeful
Player White owns 4-cube0.32480.01600.0004-0.67520.01430.0000 -0.3281 -0.2015
Standard error0.00160.00390.0003-0.00160.01150.0000 0.0066 0.0080
Player Blue owns 8-cube0.32680.01450.0005-0.67320.07930.0001 +0.0054 +0.0054
Standard error0.00220.00290.0003-0.00220.03970.0000 0.0084 0.0084
Full cubeful rollout with var.redn.
108 games, Mersenne Twister dice gen. with seed 1062244923 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Since White can't be winning all the time after rolling one of his 11/36 = 30.55% hits, he must be winning quite a few games with a second-chance shot.

Another rollout; Blue played 6-2, White redoubled and hits with 4-3:

The score (after 0 games) is: White 0, Blue 4 (match to 9 points)

Move number 9: White on roll, cube decision?

White85


2X '2X4X2X2X2X ' ' ' ' '

3O4O5O1O '2O ' ' ' ' ' '

Blue42

Position ID: 974MAACztw0AQA Match ID: EwEgAQAAIAAA

• White moves bar/21*/18

Alert: very lucky roll! ( +1.054)

# Ply Move Equity
1 R bar/21*/18 +0.6892
0.83930.02850.0002-0.16070.00150.0001 +0.6892 +0.6892
0.00300.00280.0005-0.00300.00500.0001 0.0060 0.0060
Full cubeful rollout with var.redn.
108 games, Mersenne Twister dice gen. with seed 1062244923 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
2 2 bar/21* 4/1 +0.6511 ( -0.0381)
0.8173 0.0448 0.0003 - 0.1827 0.0052 0.0000

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